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Simplifying 12v2 = 27 + 27v Solving 12v2 = 27 + 27v Solving for variable 'v'. Reorder the terms: -27 + -27v + 12v2 = 27 + 27v + -27 + -27v Reorder the terms: -27 + -27v + 12v2 = 27 + -27 + 27v + -27v Combine like terms: 27 + -27 = 0 -27 + -27v + 12v2 = 0 + 27v + -27v -27 + -27v + 12v2 = 27v + -27v Combine like terms: 27v + -27v = 0 -27 + -27v + 12v2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + -9v + 4v2) = 0 Factor a trinomial. 3((-3 + -4v)(3 + -1v)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -4v)' equal to zero and attempt to solve: Simplifying -3 + -4v = 0 Solving -3 + -4v = 0 Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4v = 0 + 3 -4v = 0 + 3 Combine like terms: 0 + 3 = 3 -4v = 3 Divide each side by '-4'. v = -0.75 Simplifying v = -0.75Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve: Simplifying 3 + -1v = 0 Solving 3 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1v = 0 + -3 -1v = 0 + -3 Combine like terms: 0 + -3 = -3 -1v = -3 Divide each side by '-1'. v = 3 Simplifying v = 3Solution
v = {-0.75, 3}
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